3 Adiabatic Expansion From the Friedmann equations, it is straightforward to appreciate that cosmic expansion is an adiabatic process: In other words, there is no ``external power responsible for pumping the tube
4 Adiabatic Expansion Thus, as we go back in time and the volume of the Universe shrinks accordingly, the temperature of the Universe goes up. This temperature behaviour is the essence behind what we commonly denote as Hot Big Bang From this evolution of temperature we can thus reconstruct the detailed Cosmic Thermal History
8 Thermal History:" Episode by Episode Planck Epoch t < sec In principle, temperature T should rise to infinity as we probe earlier and earlier into the universe s history: T, R 0 However, at that time the energy of the particles starts to reach values where quantum gravity effects become dominant. In other words, the de Broglie wavelength of the particles become comparable to their own Schwarzschild radius.
9 Thermal History: Planck Epoch Once the de Broglie wavelength is smaller than the corresponding Schwarzschild radius, the particle has essentially become a quantum black hole : de Broglie wavelength: Schwarzschild radius: These two mass scales define the epoch of quantum cosmology, in which the purely deterministic metric description of gravity by the theory of relativity needs to be augmented by a theory incorporating quantum effects: quantum gravity.
10 Thermal History: Planck Epoch On the basis of the expressions of the de Broglie wavelength and the Schwarzschild radius we may infer the typical mass scale, length scale and timescale for this epoch of quantum cosmology: Planck Mass Planck Length Planck Time Because our physics cannot yet handle quantum black holes, i.e. because we do not have any viable theory of quantum gravity we cannot answer sensibly questions on what happened before the Planck time. In other words, we are not able to probe the ultimate cosmic singularity some ideas of how things may have been do exist
11 Planck Transition In the Planck epoch, before the universe is 1 hundred-million-trilliontrillionth (10-44 ) sec old, the density reaches values higher than ρ~10 94 g/ cm 3 and temperatures in excess of T~ K. Quantum fluctuations of spacetime, on the scale of the Planck scale and Planck time are now of cosmic magnitude. Space and time are inextricably and discontinuously. As was pictured by J. Wheeler, spacetime under these conditions looks like a chaotic foam. Spacetime is a foam of quantized black holes, and space and time no longer exist in the sense that we would understand. There is no now and then, no here and there, for everywhere is torn into discontinuities. Then, due to the cosmic expansion, temperatures drop below T~10 32 K, and the unified superforce splits into a force of Gravity and a GUT force Unified Superforce Gravity Grand Unified Force
12 Thermal History:" Episode by Episode Phase Transition Era sec < t < 10-5 sec The universe is filled by a plasma of relativistic particles: quarks, leptons, gauge bosons, Higgs bosons, During this epoch, as the universe expands and cools down, it undergoes various phase transitions, as a result of Spontaneous Symmetry Breaking
13 Thermal History:" Episode by Episode Phase Transition Era sec < t < 10-5 sec We may identify three major phase transitions during this era: GUT transition z ~ Electroweak transition z ~ Quark-Hadron transition z ~ (t~10-5 s)
14 GUT Transition Before this transition, at T> GeV, there was one unified GUT force, i.e. strong, weak and electromagnetic force equally strong (note: gravity is a different case). Also, the universe did not have a net baryon number (as many baryons as antibaryons). At the GUT transition, supposedly through the Higgs mechanism, the unified GUT force splits into forces, the strong force and the electroweak force: T ~ GeV ~ K z ~
15 GUT Transition GUT Strong Force Electroweak Force Baryon non-conserving processes It is possible that the origin of the present-day excess of matter over antimatter finds its origin in the GUT phase transition. Inflationary Epoch It is conceivable that the GUT transition may be identified with the phase transition that gave rise to a rapid exponential de Sitter expansion, in which the universe expanded by ~ 60 orders of magnitude (and in which its horizon shrank accordingly). Primordial density perturbations, the seeds of cosmic structure, may have been generated during this episode.
16 Electroweak Transition T ~ 300 GeV ~ 3 x K z ~ At this energy scale, the electroweak force splits into the electromagnetic force and the weak force. Electroweak Electromagnetic Force Weak Force All the leptons acquire masses (except possibly neutrinos), intermediate vector bosons give rise to massive bosons W +, W - and Z 0, and photons.
17 Quark-Hadron Transition Above this temperature, matter in the universe exists in the form of a quark-gluon plasma. Below this temperature, isolated quarks cannot exist, and become confined in composite particles called hadrons.they combine into (quark confinement): baryons quark triplet mesons quark-antiquark pairs T ~ 0.2 GeV ~ K t ~ 10-5 sec
18 Thermal History:" Episode by Episode Hadron Era t ~10-5 sec; 300 > T > 130 MeV The hadrons formed during the quark-hadron transition are usually short-lived particles (except for protons & neutrons). Therefore, there is only a brief period in which the hadrons flourish. Although called Hadron Era, hadrons do not dominate the energy density.
19 Thermal History:" Episode by Episode Lepton Era At the beginning of the lepton era, the universe comprises: photons, baryons (small number) 10-5 sec < t < 1 min 130 > T> 0.5MeV K > T > 5x10 9 K leptons: electrons & positrons e -, e +, muons µ +, µ -, tau s τ + and τ - electron, muon and tau neutrino s
20 Thermal History:" Episode by Episode Lepton Era 10-5 sec < t < 1 min; 130 > T> 0.5MeV K > T > 5x10 9 K Four major events occur during the lepton era: Annihilation muons T ~ K Neutrino Decoupling T ~ K; z ~ Electron-Positron Annihilation T< 10 9 K; z ~ 10 9, t~1 min Primordial Nucleosynthesis T ~10 9 K; t ~ 200 sec (3 min)
21 Neutrino Decoupling T ~ K Weak interactions, e.g. t ~ 10-5 sec, z ~ get so slow that neutrinos decouple from the e +, e -, plasma. Subsequently, they proceed as a relativistic gas with its own temperature Because they decouple before the electron-positron annihilation, they keep a temperature which is lower than the photon temperature (which gets boost from released annihilation energy ): The redshift of neutrino decoupling, z~10 10, defines a surface of last neutrino scattering, resulting in a Cosmic Neutrino Background with present-day temperature T~1.95 K. A pity it is technically not feasible to see it!
22 Electron-PositronAnnihilation T < 10 9 K t ~ 1 min, z ~ 10 9 Before this redshift, electrons and photons are in thermal equilibrium. After temperature drops below T~10 9 K, the electrons and positrons annihilate, leaving a sea of photons. As they absorb the total entropy s of the e +, e -, plasma, the photons acquire a temperature T > neutrino temperaturet.
23 Electron-PositronAnnihilation At this redshift the majority of photons of the Cosmic Microwave Background are generated. These photons keep on being scattered back and forth until z ~1089, the epoch of recombination. Within 2 months after the fact, thermal equilibrium of photons is restored by a few scattering processes: free-free scattering Compton scattering T < 10 9 K t ~ 1 min, z ~ 10 9 double Compton scattering The net result is the perfect blackbody CMB spectrum we observe nowadays.
26 This is when Photons decouple from the rest of the matter and travel freely!
29 Equilibrium Processes Throughout most of the universe s history (i.e. in the early universe), various species of particles keep in (local) thermal equilibrium via interaction processes: Equilibrium as long as the interaction rate Γ int in the cosmos thermal bath, leading to N int interactions in time t, is much larger than the expansion rate of the Universe, the Hubble parameter H(t):
31 Reconstructing " Thermal History Timeline Strategy: To work out the thermal history of the Universe, one has to evaluate at each cosmic time which physical processes are still in equilibrium. Once this no longer is the case, a physically significant transition has taken place. Dependent on whether one wants a crude impression or an accurately and detailed worked out description, one may follow two approaches: q Crudely: Assess transitions of particles out of equilibrium, when they decouple from thermal bath. Usually, on crude argument: q Strictly: evolve particle distributions by integrating the Boltzmann equation
33 Thermal History: Interactions Particle interactions are mediated by gauge bosons: photons for the electromagnetic force, the W bosons for weak interactions, and gluons for the strong force (and gravitons for the gravitational force). The strength of the interaction is set by the coupling constant, leading to the following dependence of the interaction rate Γ, on temperature T: (i) mediated by massless gauge boson (photon): (ii) mediated by massive gauge boson (W +/-,Z 0 )
38 Number of protons determines element: n n n n n n n Hydrogen 1 proton Helium 2 protons Lithium 3 protons Beryllium 4 protons Boron 5 protons Carbon 6 proton Number of neutrons determines the isotope e.g., for hydrogen (1 proton), there are three isotopes n n n Normal Hydrogen (H or p) no neutrons Deuterium (d) 1 neutron Tritium (t) 2 neutrons
40 Key Fusion Reactions product: binding energy: n + p D + γ Deuterium (pn) 2.2 MeV D + D 3 He ++ + n$ % p + D 3 He ++ + γ & n + D T + γ $ ' D + D T + p % ' n + 3 He ++ T + p& 3 He (ppn) 7.72 MeV Tritium (pnn) 8.48 MeV n + 3 He ++ 4 He ++ + γ $ ' D + 3 He ++ 4 He ++ + p ' p + T 4 He ++ + γ % 4 He (ppnn) 28.3 MeV ' D + T 4 He ++ + n ' 3 He He ++ 4 He p& '
46 n n n p
48 Big Bang Nucleosynthesis Starts with Deuterium formation when the high energy tail of blackbody photons no longer breaks up D. Binding energy E=2.2 MeV. E / k T ~ ln N γ n + p D + γ ( N ) B = ln 10 9 k T ~ 0.1 MeV ( T ~ 10 9 K t ~ 100 s ) LTE+neutron decay: N p / N n ~ 7 Thus, at most, N D / N p = 1/6 ( ) ~ 20 Deuterium readily assembles into heavier nuclei.
51 Deuterium Bottleneck Note: 1) D has the lowest binding energy (2.2 MeV) (D easy to break up) 2) Nuclei with A > 2 can t form until D is produced. (requires 3-body collisions) à Deuterium bottleneck - Nucleosynthesis waits until D forms. - Then nuclei immediately form up to 4 He.
53 BBN stalls The main problem: 4 He very stable, 28 MeV binding energy. Nuclei with A = 5 are unstable! Further fusion is rare (lower binding energies): 3 He He ++ 7 Li e + + γ 3 He He ++ 7 Be γ 7 Be n 7 Li p 7 Li p 2 4 He ++ In stars, fusion proceeds because high density and temperature overcome the 4 He binding energy.
54 Primordial Abundances Because 4 He is so stable, all fusion pathways lead to 4 He, and further fusion is rare. Thus almost all neutrons end up in 4 He, and residual protons remain free. [i.e., p+p does not occur] To first order, with N p / N n ~ 7, X p Y p mass in H total mass = N p N n N p + N n = 6 8 = 0.75 mass in He total mass = 2N n N p + N n = 2 8 = 0.25 Primordial abundances of H & He (by mass, not by number).
57 Evolution of Abundances D mass fraction Be
59 Sensitivity to Parameters Abundances depend on two parameters: 1) cooling time vs neutron decay time ( proton - neutron ratio ) 2) photon-baryon ratio (T at which D forms) If cooling much faster, no neutrons decay and N p / N n ~ 5 à X p = 4/6 = 0.67 Y p = 2/6 = If cooling much slower, all neutrons decay à X p = 1 Y p = 0.
63 Baryon Density Constraint Abundances (especially D) sensitive to these 2 parameters. Why? Fewer baryons/photon, D forms at lower T, longer cooling time, more neutrons decay, less He. Also, lower density, lower collision rates, D burning incomplete, more D. Conversely, higher baryon/photon ratio -> more He and less D. Photon density is well known, but baryon density is not. à The measured D abundance constrains the baryon density!! A very important constraint. Ω b 0.04
65 fastbbn Neutron Life Time nearly all n are in 4He: Y(4He) depends on (other abundances are robust) and also on
66 Number of Light Neutrinos
72 What about Heavier Nuclei? Z = number of protons A = atomic weight = protons + neutrons As protons increase, neutrons must increase faster for stable nuclei. Nuclei with Z > 83 or >126 neutrons UNSTABLE. e.g. α-decay (emit 4 He) β-decay (emit e - )
73 α decay Photon emission
74 β decay Positron emission Electron capture